Urgent Question: Supp of a set of stochastic variables!

I have been working on understanding concept fra Measure Theory known as support or supp

I know that according to the definition

if [tex](\mathcal{X},\mathcal{T})[/tex] is a topological space and [tex](\mathcal{X},\mathcal{T}, \mu)[/tex] such that the sigma Algebra A contain all open sets [tex]U \in \mathcal{T}[/tex]. Then the support on a measure [tex]\mu[/tex] is defined as the set of all points [tex]x \in \mathcal{X} [/tex] for which every open neighbourhood of x has a positve measure